A new parallel-hat tempering algorithm has been developed for Monte Carlo simulations, in which a composite ensemble of noninteracting replicas of the molecule system at different temperatures is simulated, and the Markov process of each replica is driven by a hatlike weight factor with exponentially enhanced probability in both low- and high-energy regions. To test the algorithm, the methodology is applied to a homopolymeric protein chain located on a face-centered cubic lattice. We demonstrate that the ability of the current approach to search for low-energy molecule structures is significantly better than other Monte Carlo techniques found in the literature.